Regular Polyhedron
A regular polyhedron is a three-dimensional geometric shape where:
All the faces are congruent regular polygons (polygons with all sides and angles equal).
The same number of faces meet at each vertex (the point where edges meet).
Regular polyhedra are also known as the Platonic solids, named after the ancient Greek philosopher Plato, who studied these shapes in depth. There are exactly five regular polyhedra, and they are the only polyhedra with the properties mentioned above.
The Five Regular Polyhedra (Platonic Solids):
Tetrahedron
4 triangular faces 4 vertices 6 edges Each face is an equilateral triangle.
Cube (or Hexahedron)
6 square faces 8 vertices 12 edges Each face is a square.
Octahedron
8 triangular faces 6 vertices 12 edges Each face is an equilateral triangle.
Dodecahedron
12 pentagonal faces 20 vertices 30 edges Each face is a regular pentagon.
Icosahedron
20 triangular faces 12 vertices 30 edges Each face is an equilateral triangle.
Properties of Regular Polyhedra
All faces are